How do I measure a distance between two points?
You can use the Ruler/Protractor. As of Blender 2.80 the operator was renamed to Measure but it acts like the same way. Good news is that the Measure tool is now directly accessible from 3d View as part of the main Tool Shelf (T) and via ShiftSpacebarM hotkey.



Measure (Blender 2.80) vs Ruler/Protractor (Blender 2.79)



If you hold down Ctrl while dragging the second marker, the cursor should snap to the intersection point in order to measure the correct distance: 



With this you can also snap to the edge of the cube and set the desired length:



After that switch into Edit Mode and insert a new Edge Loop (Ctrl+R) into the right spot: 



Note: For illustration purposes I've chosen Perspective Views, but Orthographic Views probably more useful to work with in this situation.